Advice needed on who to help with jobs

I would suggest first looking at the gutter and repairing this plus adding extra ventilation should eliminate mould make sure the gutter is not leaking however if you have rising damp this would have to be treated differently furthermore anti mould paint especially designed for bathrooms

Yes looking at the guttering and the drain pipe first to see if any parts of this are damaged/leaking that could be causing the issue and also checking they are clear of any blockages as well, would certainly look at putting in a vent to give you that extra ventilation this will certainly help going forwards.There are various Anti Damp and Mould paints on the market for bathrooms just choose the best for the job you are doing.

If guttering is compromised rain water will be hitting exterior walls causing penetrating damp. Rising damp a different issue. Bathroom ventilation is essential in order to stop condensation and mould issues.

Guttering is a good idea because excess water can run into the cavity and cause severe mold . Water will go anywhere. And getting it sorted b fire the winter will stop any blockages getting frozen and may cause cracking in your guttering /down pipe

Guttering and mould clearance can be done by anyone who is competent to do so but for the bathroom fan i would suggest a qualified electrician as its wet area.

Please note that damp dose not go black and you would not get rising damp up stairs , when you get mould on the ceiling walls tiles ect it is purely moisture . first thing check outside for leaks and also check loft space to the roofing felt , also if you have had loft insulation fitted make sure they have not bridge the cavity as this prevents air to circulate in the brick around the whole building, Old type plaster boards are not as good as today's type in house either ,neither is old type plaster . check for rely good vents, also to help prevent moisture build up, fill the bath with cold water first this also stops the steam, do all this until found the problem these are the things I always carry out fist , Identify , then cure Trickle vents on UPVC widows fit new or clear old ones out Lag pipes pay attention to cold water pipes . mould is from the inside cause is 100% air born Moisture